This is one of any new mom and dad's initial fears: giving a baby their first bath. It's not as hard as some people might make it out to be; bathing a newborn is pretty simple and it gets easier as they get older. Here are a few tips for giving your baby a bath in those first few months.
First thing's first: the umbilical cord. You don't want to get this wet, so you don't want to do any actual bathing in a tub until this dries up, falls off, and the area around it is healed up. Give baby a sponge bath and wipe him off well, making sure to avoid this area until the umbilical cord is no more.
When you start regular baths, there are all types of baby bath tubs and things that you can use. If you're on the go with your little one, a collapsible tub is best. But, I personally prefer to use a sink bather in the kitchen sink, because it eliminates a lot of knee and back strain that comes with trying to do it in a normal bath tub. If you're going to use a bather in the bathtub with them instead, make sure it has a grippy type bottom to it or it can slide around and let your baby fall out of it. You may want to consider getting a collapsible baby bath tub that you can take with you anywhere. Check those out here: http://www.housemama.net/best-baby-bath-traveling/
Bathing your baby shouldn't take a lot of your time. They're fairly easy to lather up, rinse, and dry off. Most baths shouldn't take more than just a few minutes, maybe 10 at the most. But, some babies will enjoy their baths more than others. If yours enjoys a bath, let them and take your time. It's better for the baby to like the bath than learn to hate it! They also don't have to have a bath more often than 3 times a week or so.
Safety-wise, never leave your baby unattended in the tub, not even for a moment! It's far too dangerous. Babies drown in bath water all the time because a parent thought they would be gone only for a minute. If you ever think you'll be back in a minute, remember that a baby can drown in an inch of water… in under 60 seconds.